Analytical Formulas for Refractive Indices of a Telescopic GRIN Lens for Aperture Magnification

GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

“…Lastly, in (12) the initial conditions y A are assigned at the starting value of the parameter t = ψ A = ψ(r A ) by specifying the coordinates y (1:3) A = r A of the starting point A; then, from the the knowledge of the ray direction, the electric field, and the wavefront curvature at A, the rest of the vector can be completed. Namely, y = vec{n(r A ) Q(r A ) + D(r A )}, with D defined as in (8).…”

“…Finally, the Eikonal Hessian continuity provides the expression of the transmitted wave wavefront curvature dyad in which, as well as in (22), all quantities are evaluated at r A , and D i 1 (D t 2 ) is defined as in (8) with ŝi and n 1 (ŝ t and n 2 ). Equation (23) represents the generalization of the equation in [33] for the case of an interface between two homogeneous materials and reduces to it when D i 1 = D t 2 = 0.…”

“…Beam scanning can also be accomplished by altering the position or orientation of the source relative to the lens [1] or by customizing the lens distribution for multifocal capabilities. The resurgence of interest in GRIN lenses is linked to the newfound ability to manufacture them using 3D printers [2]- [8]. The two most commonly used GRIN lenses are the spherical Luneburg lens [9] and the Maxwell fisheye lens [10] , for which the refractive index is available in an analytical closed form.…”

3-D Printed All-Dielectric GRIN Lens Antenna With an Integrated Feeder

“…During the last decade, numerous studies have appeared in the literature that have qualified 3D printing as a promising technology for realizing complex 3D metamaterial structures. Starting from the characterization of the permittivity and losses for various fused filament materials [3], [4] to the realization of 3D printed structures for new antenna concepts [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. These structures range from dielectric domes [5], Modulated Dielectric Metasurfaces [6], CP polarizers [7], reflectarrays [8], [9], Risley prisms for 2D beam steering [10] and flat cylindrical [11], [12], [13], [14] and 3D GRIN lenses [15].…”

“…Starting from the characterization of the permittivity and losses for various fused filament materials [3], [4] to the realization of 3D printed structures for new antenna concepts [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. These structures range from dielectric domes [5], Modulated Dielectric Metasurfaces [6], CP polarizers [7], reflectarrays [8], [9], Risley prisms for 2D beam steering [10] and flat cylindrical [11], [12], [13], [14] and 3D GRIN lenses [15]. The principle of operation of the proposed GRIN lenses [11], [12], [13], [14] is to transform a spherical wave into a plane wave to produce highly directive beams.…”